The purpose of this application is to request career development support (two years mentored, three years independent) to acquire and develop knowledge and skills for conducting independent research on the cognitive and neuropsychological influences of math achievement among adolescents and young adults. For many individuals, the development of higher level mathematical skills and knowledge (e.g., algebra and calculus) is critical to achieving their full potential. These mathematical abilities are a manifest requirement for the development of knowledge in many disciplines including the physical and behavioral sciences, technology, and business. Algebra and calculus courses have also become a prerequisite for access to educational and economic opportunities because they are used as indicators of an individual's potential for post-secondary academic achievement. A large number of adolescents and young adults, who have not been identified as deficient in mathematical ability prior to middle and high school, fail to achieve proficiency in higher level mathematics. The goal of the career development plan is to provide the foundation for research that will identify sources of individual and developmental differences in higher level mathematical ability, determine indicators of students who may require specific intervention in order to acquire higher level math skills, and develop interventions that will improve the developmental trajectory of these students. Training will focus on five areas: (1) research methodology and statistics, (2) cognitive and neuropsychological development, (3) mathematics content and its role in other science disciplines, (4) research in schools, and (5) grant writing. The mentored and independent phase studies will focus on algebra achievement. During the mentored phase, algebra measures will be developed and tested in middle and high school algebra classes. Factor analysis will be used to determine if algebra achievement represents one or multiple constructs (e.g., procedural vs. conceptual knowledge). Item response theory will be used characterize the difficulty and discrimination of algebra items. The independent phase study will evaluate growth in algebra achievement among middle and high school students. Arithmetical ability and cognitive resources (e.g., processing speed) will be evaluated as predictors of algebra achievement.